# MandelbrotSetIterationCount

returns the number of iterations of the function , beginning with , that are needed to determine whether c is in the Mandelbrot set.

# Details and Options

• The Mandelbrot set is the set of all complex numbers c for which the sequence does not diverge to infinity when starting with .
• With the option , the sequence will be iterated at most n times to determine if the sequence diverges.
• The default setting is MaxIterations->1000.
• If the maximum number of iterations is reached, z is assumed to be in the Mandelbrot set.
• For some points that the algorithm knows in advance to be inside the Mandelbrot set, MandelbrotSetIterationCount will return one greater than the value of MaxIterations.

# Examples

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## Basic Examples(4)

Find the number of iterations needed to determine that is not in the Mandelbrot set:

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Zero is known to be inside the Mandelbrot set and therefore returns :

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It takes a few additional iterations to determine that 0.250001 is not in the Mandelbrot set:

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MandelbrotSetIterationCount works on all kinds of numbers:

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# See Also

Introduced in 2014
(10.0)